We investigate the scalar field equation in a (2+1) -dimensional charged BTZ black hole. The quasinormal spectra of the solution are obtained applying two different methods and good convergence between both is achieved. Using the characteristic integration technique we tested the geometry evidencing its stability against linear scalar perturbations. As a consequence a two pattern set of frequencies (families) emerges, one oscillatory and another purely imaginary. In that spectra, the fundamental modes without angular momentum are hugely affected by the presence of the black hole charge surprisedly even for small values of this. Their evolution are controlled by purely imaginary frequencies as in the non-rotating chargeless BTZ case. Similar to others AdS black holes, the fundamental oscillations scale the black hole event horizon and the temperature of the hole (far from maximal charges).

中文翻译：

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带电 BTZ 黑洞的拟正态模式


我们研究了 (2+1) 维带电 BTZ 黑洞中的标量场方程。采用两种不同的方法获得了解的拟正规谱，并且两者取得了良好的收敛性。使用特征积分技术，我们测试了几何结构，证明其对线性标量扰动的稳定性。结果，出现了两种模式的频率（族），一种是振荡的，另一种是纯虚数的。在该光谱中，即使黑洞电荷的值很小，没有角动量的基本模式也会受到黑洞电荷的存在的巨大影响。它们的演变完全由虚数频率控制，如非旋转无电荷 BTZ 情况。与其他 AdS 黑洞类似，基本振荡会缩放黑洞事件视界和黑洞温度（远离最大电荷）。